Application of modern control theory in portfolio optimization

This dissertation focuses on applying modern control theory, specifically robust control and receding horizon control, to problems in portfolio optimization.; In the first part of the dissertation, we formulate an enhanced index tracking problem under continuous time dynamics and uncertain parameters, the mean rates of return and the covariance matrix. Norm bounded uncertainty is used as the uncertainty structure for applying robust control methods. The problem is reduced to the solution of a modified generalized Riccati equation which is approximated by a homotopy method and linearization, and solved by successive semidefinite programs.; Computational results using historical data for estimating the mean returns and the covariance matrix show that the solution to the robust problem performs better than that of the non-robust problem when there is a large difference between estimated parameters and realized parameters. Also, the robust portfolio decreases the volatility of the tracking error, compared to the non-robust portfolio where uncertainty in mean returns is not considered.; In the second part of the dissertation, we develop stochastic receding horizon control as a suboptimal approach to constrained portfolio optimization. Receding horizon control is a technique that numerically solves on-line finite horizon optimization problems to determine a control strategy. We first examine the theoretical performance bound of the stochastic receding horizon implementation, based upon the stability results. We establish theoretical results on mean performance as well as constraint satisfaction.; We then use stochastic receding horizon control as a suboptimal approach to an infinite horizon constrained portfolio optimization problem. The dynamics are lifted to handle constraints that involve state and control information at different points in time, and the finite horizon optimization problems in receding horizon control can be written as a semidefinite program under the structure of innovations feedback. Computational results using historical data show that stochastic receding horizon control is a promising approach in solving difficult portfolio optimization problems with constraints.